Sampling Designs for Estimating Spatial Variance Components

Sampling designs and estimation procedures are considered for the spatial variogram when no information on magnitude or scale of variation of a spatial variable is available. Design-based solutions to this problem have involved nested balanced designs and estimation based on the method of moments for a random effects model. It has been suggested that highly unbalanced staggered designs may be more efficient in terms of sampling effort than balanced nested designs. All the previous methods based on the estimation of variance components are essentially non-spatial, however. Practical, spatial and parsimonious considerations lead us to a hybrid design-model-based approach of staggered designs on linear transects in three orientations as a suitable sampling procedure

[1]  W. Youden,et al.  Selection of Efficient Methods for Soil Sampling1 , 1938 .

[2]  G. H. Jowett SAMPLING PROPERTIES OF LOCAL STATISTICS IN STATIONARY STOCHASTIC SERIES , 1955 .

[3]  W. C. Krumbein,et al.  STATISTICAL ANALYSIS OF LOW-LEVEL RADIOACTIVITY OF PENNSYLVANIAN BLACK FISSILE SHALE IN ILLINOIS , 1956 .

[4]  W. R. Buckland,et al.  A dictionary of statistical terms , 1958 .

[5]  H. L. Lucas,et al.  DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS , 1959 .

[6]  John C. Gower Variance component estimation for unbalanced hierarchical classifications , 1962 .

[7]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[8]  R. Mead,et al.  A test for spatial pattern at several scales using data from a grid of contiguous quadrats. , 1974 .

[9]  A. T. Miesch Variograms and Variance Components in Geochemistry and Ore Evaluation , 1975 .

[10]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[11]  D. Harville Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[12]  B. Mandelbrot Fractal Geometry of Nature , 1984 .

[13]  S. Nortcliff,et al.  SOIL VARIABILITY AND RECONNAISSANCE SOIL MAPPING. A STATISTICAL STUDY IN NORFOLK , 1978 .

[14]  N. Cressie,et al.  Robust estimation of the variogram: I , 1980 .

[15]  Alex B. McBratney,et al.  The design of optimal sampling schemes for local estimation and mapping of regionalized variables—II: Program and examples☆ , 1981 .

[16]  Alex B. McBratney,et al.  The design of optimal sampling schemes for local estimation and mapping of of regionalized variables—I: Theory and method , 1981 .

[17]  David Russo,et al.  Design of an Optimal Sampling Network for Estimating the Variogram , 1984 .

[18]  K. Mardia,et al.  Maximum likelihood estimation of models for residual covariance in spatial regression , 1984 .

[19]  Margaret A. Oliver,et al.  Combining Nested and Linear Sampling for Determining the Scale and Form of Spatial Variation of Regionalized Variables , 2010 .

[20]  A. Warrick,et al.  Optimization of Sampling Locations for Variogram Calculations , 1987 .

[21]  Christopher J. Nachtsheim,et al.  Diagnostics for mixed-model analysis of variance , 1987 .

[22]  Interpolation and optimal linear prediction , 1989 .

[23]  Alex B. McBratney,et al.  Further Comparison of Spatial Methods for Predicting Soil pH , 1990 .

[24]  C. Braak,et al.  Model-free estimation from spatial samples: A reappraisal of classical sampling theory , 1990 .

[25]  Alex B. McBratney,et al.  Estimation and implications of instrumental drift, random measurement error and nugget variance of soil attributes-a case study for soil pH. , 1990 .

[26]  Dale L. Zimmerman,et al.  A comparison of spatial semivariogram estimators and corresponding ordinary Kriging predictors , 1991 .

[27]  Graham J. Wills,et al.  Dynamic Graphics for Exploring Spatial Data with Application to Locating Global and Local Anomalies , 1991 .